I assume by "private" it mean the house has a pool right at the house just for people at the house vs a community pool/hot tub
We stayed at a house that was 5 minuntes from Animal Kingdom (so closer than some of the resorts) had 8 bedrooms, it's own pool - plus the community had a pool and hot tub and tiki bar with food. Highly themed rooms (to Disney and Universal) and was $220 a night (probably a little more now, this was a few years ago)
If you have a decent sized group a house can make a ton of sense, but are downsides of course ... most likely need a car (or else spending a lot on Uber, etc), if something goes wrong, uncertainty around fixing it,
Like everything, there are pros and cons and people weight things differently